| { | |
| "name": "graceful_graph_k2_p3__v0_h", | |
| "problem_type": "graceful_graph", | |
| "params": { | |
| "k": 2, | |
| "p": 3 | |
| }, | |
| "prompt": "Find a graceful labeling for the graph G_{2,3}: 3 disjoint K_2 cliques (numbered 0 through 2), where each pair of consecutive cliques (g, g+1) is connected by 2 edges that link vertex i of clique g to vertex i of clique g+1 for each i in 0..1. The graph has 6 vertices and 7 edges in total.\n\nA graceful labeling assigns each vertex a unique label from 0 to 7 such that all edge labels |label(u) - label(v)| are distinct.\n\nReturn a list of 6 integers giving the vertex labels, ordered by clique then vertex within clique (so the i-th block of 2 consecutive entries gives the labels for clique i), or state \"UNSATISFIABLE\" if no such labeling exists.\n\nPartial assignment (fixed values that must be respected):\n- x[2]=7\n- d[6]=3\nReturn a complete solution consistent with these fixed assignments.", | |
| "satisfiable": true, | |
| "solution": { | |
| "x": [ | |
| 0, | |
| 2, | |
| 7, | |
| 3, | |
| 1, | |
| 6 | |
| ], | |
| "d": [ | |
| 2, | |
| 4, | |
| 5, | |
| 7, | |
| 1, | |
| 6, | |
| 3 | |
| ] | |
| }, | |
| "difficulty": { | |
| "solve_time_ms": 1025.2, | |
| "search_space": 262144, | |
| "num_variables": 13, | |
| "num_constraints": 11, | |
| "num_edges": -1, | |
| "backend": "pycsp", | |
| "solve_tier": "hard", | |
| "solve_pct_global": 72.37, | |
| "solve_pct_type": 18.75 | |
| }, | |
| "partial_assignment": { | |
| "x": { | |
| "2": 7 | |
| }, | |
| "d": { | |
| "6": 3 | |
| } | |
| } | |
| } |